if `a gt c`, show that abc - cba = 99(a - c)

If a=c, show that cba-abc=0

If c gt a , show that cba-abc=99(c-a)

Let a,b,c in R and a gt 0 . If the quadratic equation ax^(2) +bx +c=0 has two real roots alpha and beta such that alpha gt -1 and beta gt 1 , then show that 1 + |b/a| + c/a gt 0

In a Delta ABC, show that (a cos A+b cos B+ c cos C)/(a+b+c)= (r )/(R )

If a+ b + c = 0 , show that : a^(3) + b^(3) + c^(3)= 3abc

If vec c = 3vec a+4vec b and 2vec c =vec a -3vec b , show that (i) vec c and vec a have the same direction and |vec c| gt |vec a| (ii) vec b and vec c have opposite direction and |vec c| gt |vec b|

In any Delta ABC, show that cos A+ cos B+ cos C = (1+ (r )/(R )).

If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]| =0, show that abc(ab+bc+ac) = a+b+c

If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]| =0, show that abc(ab+bc+ac) = a+b+c

If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]| =0, show that abc(ab+bc+ac) = a+b+c